class_docstr: Class for the ProductHPDMatricesAndSiegelDisks manifold.
  
  The HPD and Siegel product manifold is a direct product of the HPD manifold
  and (n-1) Siegel disks. Each manifold of the product is a square matrix
  manifold of the same dimension.
  
  Parameters
  ----------
  n_manifolds : int
      Number of manifolds of the product.
  n : int
      Size of the matrices.
code: def __init__(self, n_manifolds, n, equip=True):
      self.n_manifolds = n_manifolds
      self.n = n
  
      factors = [HPDMatrices(n=n, equip=False)] + [
          Siegel(n=n, equip=False) for _ in range((n_manifolds - 1))
      ]
  
      scales = [
          float(n_manifolds - i_manifold)
          for i_manifold in range(n_manifolds)
      ]
      factors[0].metric = ScalarProductMetric(
          HPDAffineMetric(factors[0]), scales[0]
      )
      for factor, scale in zip(factors[1:], scales[1:]):
          factor.metric = ScalarProductMetric(
              SiegelMetric(factor), scale
          )
  
      super().__init__(
          factors=factors,
          default_point_type="other",
          equip=equip,
      )
  
file_path: geomstats/geomstats/geometry/product_hpd_and_siegel_disks.py
imports: from geomstats.geometry.hpd_matrices import HPDAffineMetric, HPDMatrices
  from geomstats.geometry.product_manifold import ProductManifold, ProductRiemannianMetric
  from geomstats.geometry.scalar_product_metric import ScalarProductMetric
  from geomstats.geometry.siegel import Siegel, SiegelMetric
label_desc: Use image node_id 1 to create a new ProductHPDMatricesAndSiegelDisks object from inherited base classes: ProductManifold with example: obj = ProductHPDMatricesAndSiegelDisks(n_manifolds, n, equip)